Very little, I should imagine, since practically every "partial victory" is immediately overturned by the Death Eater courts. I'd like to know of a specific instance in which a law was defeated by "pro-life dogmatists" in one jurisdiction, while being passed and upheld by courts in another.
I don’t know that there’s an instance of any partial victory on abortion being defeated by people backing an all-or-nothing pro-life view. What I DO know is manifest in a quite pointed question asked by Supreme Court Justice Antonin Scalia. He said, “I am against abortion, but where is the moral outcry in America?”
Imagine it: a Judge in the highest Court in this country chastising The Church on an issue where the voice of The Church should be drowning out all others, but isn’t, and I think that this is how the courts have come to think that they have cover when they overturn the partial victories they have.
So, It’s not so much direct opposition to partial victory that has cost lives, but the perception of merely lukewarm support.